Coalitional Games on Graphs: Core Structure, Substitutes

2012

We analyze an infinite horizon, non-cooperative bargaining model for TU games with general coalitional structure. In each period of the game an opportunity for a feasible coalition to form arises according to a stochastic process, and a randomly selected agent in the coalition makes a take-it-or-leave-it offer. Agents that reach an agreement exit the game and are replaced by clones. We characterize the set of stationary equilibria by a convex program. We examine the implications of this characterization when the feasible coalitions are determined by an underlying network. We show how an agent's payoff is related to the centrality of his position in the network.

Mathematical Social Sciences, 2015

Coalitional network games are real-valued functions defined on a set of players organized into a network and a coalition structure. We adopt a flexible approach assuming that players organize themselves the best way possible by forming the efficient coalitional network structure. We propose two allocation rules that distribute the value of the efficient coalitional network structure: the atom-based flexible coalitional network allocation rule and the player-based flexible coalitional network allocation rule.

2009

2010

Abstract. In this paper we propose a novel approach to represent coalitional games, called a Coalition-Flow Network (CF-NET), that builds upon a generalization of the network flow literature. Specifi-cally, this representation is based on our observation that the coalition ...

cgi.di.uoa.gr

2013

Coalitional network games are real-valued functions defined on a set of players organized into a network and a coalition structure. We adopt a flexible approach assuming that players organize themselves the best way possible by forming the efficient coalitional network structure. We propose two allocation rules that distribute the value of the efficient coalitional network structure: the atombased flexible coalitional network allocation rule and the player-based flexible coalitional network allocation rule.

2008 3rd International Symposium on Communications, Control and Signal Processing, 2008

We develop a unifying analytical and optimizationbased framework for the design, operation and performance evaluation of networks of dynamic autonomous agents. The fundamental view is that agents in such a network are dynamic entities that collaborate because via collaboration they can accomplish objectives and goals much better than working alone, or even accomplish objectives that they cannot achieve alone at all. Yet the benefits derived from such collaboration require some costs (e.g. communications), or equivalently, the collaboration is subject to constraints. Understanding and quantifying this tradeoff between the benefits vs the costs of collaboration, leads to new methods that can be used to analyze, design and control/operate networks of agents. Although the inspiration for the framework comes from social and economic networks, the fundamental ideas and in particular the methodology of dynamic constrained coalitional games (DCCG) can unify many concepts and algorithms for networks in various areas: social networks, communication networks, sensor networks, economic networks, biological networks, physics networks. We then analyze a specific instance of such tradeoffs arising in the design of security aware network protocols. We extend network utility maximization (NUM) so as to encompass security metrics such as "trust". The trust values assigned to nodes are based on interaction history and community-based monitoring. The effect of these trust values on the resulting protocols is that in routing and media access scheduling node trustworthiness is automatically considered and used. We develop a distributed algorithm for the joint physical-MAC-routing protocol design. Our extension to NUM with security concerns leads to resilient networks.

2017

A divisible resource needs to be divided amongst the agents in a society who are connected in a network. Agents care about the amount of money they receive as well as the amounts that their neighbors receive. The existence (or non-existence) of a link between a pair of agents is private information of these two agents. We introduce and characterize the class of strategy-proof mechanisms for different shapes in the utility function.

Artificial Intelligence, 2010

Coalitional Resource Games (crgs) are a form of Non-Transferable Utility (ntu) game, which provide a natural formal framework for modelling scenarios in which agents must pool scarce resources in order to achieve mutually satisfying sets of goals. Although a number of computational questions surrounding crgs have been studied, there has to date been no attempt to develop solution concepts for crgs, or techniques for constructing solutions. In this paper, we rectify this omission. Following a review of the crg framework and a discussion of related work, we formalise notions of coalition structures and the core for crgs, and investigate the complexity of questions such as determining nonemptiness of the core. We show that, while such questions are in general computationally hard, it is possible to check the stability of a coalition structure in time exponential in the number of goals in the system, but polynomial in the number of agents and resources. As a consequence, checking stability is feasible for systems with small or bounded numbers of goals. We then consider constructive approaches to generating coalition structures. We present a negotiation protocol for crgs, give an associated negotiation strategy, and prove that this strategy forms a subgame perfect equilibrium. We then show that coalition structures produced by the protocol satisfy several desirable properties: Pareto optimality, dummy player, and pseudo-symmetry.

2004

In an abstract model of division problems, we study division rules that are not manipulable through a reallocation of individual characteristic vectors within a coalition (e.g. reallocation of claims in bankruptcy problems). A coalition can be formed under a given communication network, a (non-directed) graph, if members of this coalition are connected on the graph. We offer a characterization of nonmanipulable division rules without any assumption on the graph structure. When the graph is complete, this result reduces to the results established by previous authors. We also consider other special cases such as trees and graphs without a "bridge". The family of reallocation-proof rules can get larger or smaller depending on the graph structure. Our abstract model can have various special examples such as bankruptcy, surplus sharing, cost sharing, income redistribution, social choice with transferable utility, etc.